|EFF Offers Awards for Large Composite Numbers
||[Apr. 1st, 2009|08:34 pm]
Inspired by the attention its Cooperative Computing Awards|
has brought to the power of collaboration to solve
difficult mathematics problems, EFF today announced a new
award. EFF will offer three increasing rewards of $6, $8,
and $12 to the persons or team who, working
collaboratively, can discover a world-record composite
Composite numbers are those which are divisible by some
whole number other than themselves and one. Familiar
examples include 8, 100, 525, and 4294967296. Notably, all
even numbers greater than 2 are composite. Composite
numbers have important applications in engineering,
scientific research and even finance, where they are often
used to measure enormously large values with a high degree
of precision. Composite numbers are surprisingly common—indeed, most numbers are composite—but naming extremely
large composite numbers can become a daunting task.
However, throughout human history, the largest known
composite number has consistently been larger than the
largest known prime number. Indeed, this trend is likely to
continue. The world’s largest known primes have for some
time been Mersenne primes; but to every Mersenne number
2^p-1 where p is a prime, there corresponds a larger
composite number 2^p-1+1.
In 2007, two philosophers competed in an event under the
auspices of the Massachusetts Institute of Technology to
see who could name the largest number using only an
ordinary chalkboard. The winning number, found by Prof.
Adam N. Elga, was almost certainly composite.
“Huge composite numbers are all around us, but very few
people have ever even tried to name a number larger than a
googol,” said EFF Staff Technologist Seth Schoen.
“Hopefully this contest will remedy that and maybe even set
a few records in the process.”
A proof attributed to the Greek mathematician Euclid shows
that there is no largest composite number. Euclid suggests
multiplying all known whole numbers together and then
failing to add one. The result will be divisible by “lots
of stuff,” and hence composite.
EFF’s new awards program was established with funds found
under a couch cushion one day here at the EFF office.
Prospective claimants will—as with EFF’s Cooperative
Computing Awards—need to publish their results in a
peer-reviewed scientific journal, including rigorous proof
that the numbers they are claiming are not prime. The proof
must also show that a claimed composite number is larger
than Prof. Elga’s 2007 record. EFF also reserves the right
to require that claimants explicitly identity at least one
specific divisor of a claimed composite number.